All was hushed just before dawn when Debbie Gabriel double-parked at her usual spot on Lefferts Avenue, a neighborhood of single-family homes and low apartment blocks in Flatbush, Brooklyn. Almost as soon as she turned off the ignition, street cats in all shades and sizes started pouring out from an alley behind a tall iron gate like extras in a zombie movie.

A dozen cats in all stood there, softly purring for their breakfast, as Ms. Gabriel set out bowls of food and water on the pavement.

It was a familiar scene for Ms. Gabriel, who has been a caretaker of numerous cat colonies over the past 23 years. “There are days when I don’t want to get up,” she said. “But when I think of their little faces — if they can stand there at 4:30 in the morning and wait for me, the least I can do is show up for these babies.”

The problem is hardly limited to Flatbush. There are colonies in virtually every neighborhood with suitable nooks and crannies — in Bushwick, in Washington Heights, in Ozone Park. There may be as many as half a million feral cats padding around New York City, but no one knows for sure.

“No one knows, and the city doesn’t care to know,” said Will Zweigart, the founder of Flatbush Cats, the nonprofit group that Ms. Gabriel and scores of others volunteer with. “Because if they knew, they would be accountable to do something about it.”

There are a number of reasons for the explosion in feral cat colonies. More people adopted pets during the pandemic, but keeping them soon became difficult. For one thing, pets are more expensive now. New York City — along with the rest of the country — faces a severe shortage of veterinarians, many of whom were overwhelmed and burned out by the high demand for their services, and veterinary fees have outpaced the average rate of inflation for the past 20 years.

Add to that the expiration of eviction moratoriums and other pandemic economic protections, and many New Yorkers simply can’t afford their pets anymore. Some people, fearing that their unwanted cats would be euthanized if they were taken to a shelter, simply let them out on the streets and hoped for the best.

This is where self-appointed colony caretakers like Ms. Gabriel — she takes pride in the title “cat lady” — devote their efforts. “Everyone on my block comes to me when they have a cat issue,” she said. People mostly appreciate her efforts, but a few are hostile to the cats, especially in late spring, the height of breeding season, when unfixed and sex-starved beasts yowl and fight over mates. (One reason she visits her colony so early in the morning is to avoid unpleasant encounters with neighbors.)

Ms. Gabriel’s vigilance has helped her save some cats from a sad end. She recalled seeing a man crossing the street one summer morning lugging a big cardboard box. “I asked him what he had in the box,” she said. “He opened it up and there were five kittens inside. His girlfriend had told him that they couldn’t keep them.”

The temperature was over 90 degrees. The kittens would have been dead in an hour if they were left on the street as planned. Ms. Gabriel snatched the box from him. She found homes for three of the kittens and adopted the other two herself. “I told the guy how important it was to neuter his cats, both for the cats’ sake and for the sake of the neighborhood,” she recalled. Then she arranged for a veterinarian to visit the man’s apartment and neuter his two remaining house cats.

Naturally, not everyone is thrilled with clusters of wild cats, particularly New York’s many birders — a population that also bloomed during the pandemic. Grant Sizemore, the director of invasive species programs at the American Bird Conservancy, estimated that outdoor cats kill 2.4 billion birds annually in the United States. “We don’t allow stray and feral dogs to roam the landscape,” Mr. Sizemore said. “And we shouldn’t allow it for cats either. It’s not safe for the cats, and it’s certainly not safe for the birds and other wildlife.”

Do feline predatory instincts have an upside? While New York’s feral cats kill lots of mice, they are no match for the city’s rats, which greatly outnumber them. Popular notions aside, cats rarely attack rats, though rodents do avoid nesting near often-pungent cat colonies.

But even most cat caretakers say they would far prefer that all cats lived indoors. “New Yorkers have no idea how difficult it is to be a street cat,” said Rachel Adams, a cat trapper for Flatbush Cats and a clinical psychologist at Kingsboro Psychiatric Center.

Mr. Zweigart unequivocally calls it “a crisis.” There are way too many cats outdoors, he said, and too few people willing to offer the friendly ones a place to live. “We cannot adopt our way out of this problem. That’s a Band-Aid at best.”

So under Mr. Zweigart’s leadership, Flatbush Cats has adopted a somewhat radical idea that was first developed in England in the 1950s to deal with a feral cat problem: T.N.R. — trap, neuter, return. Volunteers who have been certified in the procedure capture feral cats in animal traps, then bring them to veterinarians to be fixed. The cats are then released back to the streets to live out their lives, but without leaving litters behind. In theory, T.N.R. should gradually deplete and eventually eliminate the city’s cat colonies.

Animal protection groups like PETA and the ASPCA advocate T.N.R., and cities from Chicago to Jacksonville, Fla., have passed local ordinances supporting it. On the other hand, organizations like the Audubon Society and the Cornell Lab of Ornithology oppose the method, holding that cats are a highly destructive invasive species that should not be allowed to live outdoors at all. They also say there is no solid evidence that T.N.R. has actually lowered outdoor cat populations anywhere that it is being practiced.

But while Flatbush Cats trains volunteers in trap-neuter-release, the city Health Department and the Mayor’s Office of Animal Welfare have been slow to get behind the protocol, neither prohibiting nor advocating it, and offering its practitioners little material support.

With the city taking a back seat, it has been left to nonprofits like Flatbush Cats to take up the slack. The organization is building a 3,700-square-foot veterinary clinic on Flatbush Avenue, which will open in August. The aim is to provide thousands of low-cost spay-and-neuter surgeries a year for cats whose owners often can’t afford to take them to commercial veterinarians, where the procedures can cost more than $500.

Still, not everybody in Flatbush is on board with this approach, according to Ryan Tarpey, the community program manager for Flatbush Cats. When Mr. Tarpey set out traps near of one notorious cat colony that had been residing in an empty lot for 47 years, some neighbors were outraged. “They told me, ‘These are our cats, they’ve been keeping the rats out,’” he said. “They ran me off the block.”

Even some caretakers are initially hesitant to set out cat traps. “Some people prefer to let the colony continue to procreate,” Ms. Adams, a Baltimore native who relocated to New York seven years ago, confirmed. “But most long-term caretakers have had so many bad experiences where they found dead cats or kittens, or their cats came back sick or injured,” she added. “Usually when that happens, they change their tone.”

Rob Holden, a 35-year-old account manager in the publishing industry who recently began volunteering with Flatbush Cats, is such a convert. Earlier this spring, Mr. Holden noticed an orange tabby lurking in a garage in the alley behind his apartment in Flatbush. The animal had a pronounced limp, and like most longtime street cats, it seemed wary of humans, and wouldn’t let him get close. So Mr. Holden jury-rigged a food-laden steel trap with a trip wire dangling from his second-story apartment. He also set up two motion-sensing cameras that would alert him when the cat approached.

It took four days, but when the cat finally worked up the courage to enter the trap, Mr. Holden was ready, yanking the trip wire and quickly whisking the creature off to a garage that Flatbush Cats has repurposed as a holding area for strays.

Its injuries were so severe (most likely from a fight with another cat) that in any other hands, the cat — now named Ramones — probably would have been euthanized. But volunteers took Ramones to a veterinarian who managed to patch him up with 14 stitches and a round of antibiotics.

The next step took longer. Ramones was not accustomed to living with humans. The process of getting street cats comfortable around people is labor-intensive, requiring hours of painstaking seduction. It doesn’t always work, but in this case it succeeded.

“Ramones is now without doubt one of the friendliest (and hungriest) cats I had ever met,” Mr. Holden said with real affection. “He’s recovering with a lovely foster couple. Needless to say, my first trapping experience has me hooked.”